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4.2 Exercises

From Förberedande kurs i matematik 1

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{{Ej vald flik|[[4.2 Trigonometriska funktioner|Theory]]}}
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{{Vald flik|[[4.2 Övningar|Exercises]]}}
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</div>{{#NAVCONTENT:Answer|Svar 4.2:1|Solution a |Lösning 4.2:1a|Solution b |Lösning 4.2:1b|Solution c |Lösning 4.2:1c|Solution d |Lösning 4.2:1d|Solution e |Lösning 4.2:1e|Solution f |Lösning 4.2:1f}}
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</div>{{#NAVCONTENT:Answer|Answer 4.2:1|Solution a |Solution 4.2:1a|Solution b |Solution 4.2:1b|Solution c |Solution 4.2:1c|Solution d |Solution 4.2:1d|Solution e |Solution 4.2:1e|Solution f |Solution 4.2:1f}}
===Exercise 4.2:2===
===Exercise 4.2:2===
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|width="50%" | {{:4.2 - Figur - Likbent triangel med toppvinkeln v och sidor 2, 3 och 3}}
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</div>{{#NAVCONTENT:Answer|Svar 4.2:2|Solution a |Lösning 4.2:2a|Solution b |Lösning 4.2:2b|Solution c |Lösning 4.2:2c|Solution d |Lösning 4.2:2d|Solution e |Lösning 4.2:2e|Solution f |Lösning 4.2:2f}}
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</div>{{#NAVCONTENT:Answer|Answer 4.2:2|Solution a |Solution 4.2:2a|Solution b |Solution 4.2:2b|Solution c |Solution 4.2:2c|Solution d |Solution 4.2:2d|Solution e |Solution 4.2:2e|Solution f |Solution 4.2:2f}}
===Exercise 4.2:3===
===Exercise 4.2:3===
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</div>{{#NAVCONTENT:Answer|Svar 4.2:3|Solution a |Lösning 4.2:3a|Solution b |Lösning 4.2:3b|Solution c |Lösning 4.2:3c|Solution d |Lösning 4.2:3d|Solution e |Lösning 4.2:3e|Solution f |Lösning 4.2:3f}}
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</div>{{#NAVCONTENT:Answer|Answer 4.2:3|Solution a |Solution 4.2:3a|Solution b |Solution 4.2:3b|Solution c |Solution 4.2:3c|Solution d |Solution 4.2:3d|Solution e |Solution 4.2:3e|Solution f |Solution 4.2:3f}}
===Exercise 4.2:4===
===Exercise 4.2:4===
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|width="33%" | <math>\tan{\left(-\displaystyle \frac{5\pi}{3}\right)}</math>
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</div>{{#NAVCONTENT:Answer|Svar 4.2:4|Solution a |Lösning 4.2:4a|Solution b |Lösning 4.2:4b|Solution c |Lösning 4.2:4c|Solution d |Lösning 4.2:4d|Solution e |Lösning 4.2:4e|Solution f |Lösning 4.2:4f}}
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</div>{{#NAVCONTENT:Answer|Answer 4.2:4|Solution a |Solution 4.2:4a|Solution b |Solution 4.2:4b|Solution c |Solution 4.2:4c|Solution d |Solution 4.2:4d|Solution e |Solution 4.2:4e|Solution f |Solution 4.2:4f}}
===Exercise 4.2:5===
===Exercise 4.2:5===
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</div>{{#NAVCONTENT:Answer|Svar 4.2:5|Solution a |Lösning 4.2:5a|Solution b |Lösning 4.2:5b|Solution c |Lösning 4.2:5c|Solution d |Lösning 4.2:5d}}
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</div>{{#NAVCONTENT:Answer|Answer 4.2:5|Solution a |Solution 4.2:5a|Solution b |Solution 4.2:5b|Solution c |Solution 4.2:5c|Solution d |Solution 4.2:5d}}
===Exercise 4.2:6===
===Exercise 4.2:6===
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</div>{{#NAVCONTENT:Answer|Svar 4.2:6|Solution |Lösning 4.2:6}}
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===Exercise 4.2:7===
===Exercise 4.2:7===
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</div>{{#NAVCONTENT:Answer|Svar 4.2:7|Solution |Lösning 4.2:7}}
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===Exercise 4.2:8===
===Exercise 4.2:8===
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===Exercise 4.2:9===
===Exercise 4.2:9===
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Current revision

       Theory          Exercises      

Exercise 4.2:1

Using the trigonometric functions, determine the length of the side markedx

a)

[Image]

b)

[Image]

c)

[Image]

d)

[Image]

e)

[Image]

f)

[Image]

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:2

Determine a trigonometric equation that is satisfied by v.

a)

[Image]

b)

[Image]

c)

[Image]

d)

[Image]

e)

[Image]

f)

[Image]

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:3

Determine

a) sin−2  b) cos2 c) sin9
d) cos27 e) sin43 f) cos−6 

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:4

Determine

a) cos611 b) cos311 c) tan43
d) tan e) tan67 f) tan−35 

Answer | Solution a | Solution b | Solution c | Solution d | Solution e | Solution f

Exercise 4.2:5

Determine

a) cos135 b) tan225 c) cos330 d) tan495

Answer | Solution a | Solution b | Solution c | Solution d

Exercise 4.2:6

Determine the length of the side marked x.

[Image]

Answer | Solution

Exercise 4.2:7

In order to determine the width of a river, we measure from two points, A and B on one side of the straight bank to a tree, C, on the opposite side. How wide is the river if the measurements in the figure are correct?

[Image]

Answer | Solution

Exercise 4.2:8

A rod of length hangs from two ropes of length a and b as shown in the figure. The ropes make angles and with the vertical. Determine a trigonometric equation for the angle which the rod makes with the vertical.

[Image]

Answer | Solution

Exercise 4.2:9

The road from A to B consists of three straight parts AP, PQ and QB, which are 4.0 km, 12.0 km and 5.0 km respectively. The angles marked at P and Q in the figure are 30° and 90° respectively. Calculate the distance as the crow flies from A to B. (The exercise is taken from the Swedish National Exam in Mathematics, November 1976, although slightly modified.)

[Image]

Answer | Solution

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